Nine Chapters on the Mathematical Art

《九章算术》 c. 1st century · compiled in the Eastern Han

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Overview

The foundation of ancient Chinese mathematics; the methods of its chapters on equitable transport and on excess and deficit are the arithmetic basis of calendrical computation.

Key data

ItemDetail
Completedc. 1st century (Eastern Han), compiled from earlier Qin and Han works
StructureNine chapters, 246 problems
FormEach problem with its question, answer and method
PredecessorFollows the “Book of Numbers” from the Zhangjiashan Han slips

The contents of the nine chapters

The work is divided into nine chapters — rectangular fields, millet and rice, proportional division, diminishing breadth, consultation on works, equitable transport, excess and deficit, the rectangular array, and the right triangle —

each problem with its question, answer and method.

Its structure follows the “Book of Numbers” from the Zhangjiashan Han slips, but its system is more complete and its problems more numerous.

Its link with the calendar

The fractions, common denominators, proportions and methods of excess and deficit on which calendrical computation depends

all appear in its chapters.

New moons, intercalary remainders and grand epochs cannot be computed without arithmetic of this kind.

That the Chinese joined “calendar” and “calculation” in one phrase rests on this.

Value

The Nine Chapters is the backbone of ancient Chinese mathematics;

the mathematical works of the following thousand years developed within its frame.

Liu Hui is the most famous of its commentators, and his commentary is a classic of Chinese mathematics alongside the text itself.

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Compiled and arranged by Chujia Kuang.

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